Forward and inverse transforms of multi-dimensional groups of time domain or frequency domain coefficients representative of a video signal or signals are important operations in proposed high definition television (HDTV) systems and multimedia systems.
Typically at a transmitter a video signal in the time domain is broken down into discrete time domain coefficients representative of the video signal. The time domain coefficients are forward transformed into frequency domain coefficients. The high frequency components can be deleted to compress the video signal. At a video receiver, such as a television, the frequency domain coefficients are inversely transformed to time domain coefficients and the time domain coefficients are used to form a video signal on the television display. The time domain and the frequency domain coefficients are digital signals in and of themselves.
Two-dimensional inverse and forward discrete cosine transforms are particularly important for systems which comply with video compression standards such as Joint Picture Expert Group (JPEG) and Motion Picture Expert Group (MPEG). However, both forward and inverse transforms are computationally intensive and difficult to implement in very large scale integrated circuits (VLSI) using direct matrix multiplication.
Knauer et al. ("Knauer") discloses an apparatus for performing a forward and inverse two-dimensional discrete cosine transform in U.S. Pat. No. 4,829,465. (See col. 1, lns. 8-9) In FIG. 1 of that patent, Knauer shows a block diagram for a two-dimensional forward discrete cosine transformer comprised of a first transposition stage and two consecutive one-dimensional transformers separated by a second transposition stage. Knauer further discloses a one-dimensional transformer which reduces the number of multiplications required by prior one-dimensional transformers by taking advantage of the symmetry in a transform matrix.